Generalizations and specializations of generating functions for Jacobi,\n Gegenbauer, Chebyshev and Legendre polynomials with definite integrals

2012/09/28 by Howard S. Cohl, Cohl, Howard, Connor MacKenzie +1 · 1 citation
Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Iterative Methods for Nonlinear Equations #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.1210.0039

Abstract

In this paper we generalize and specialize generating functions for classical\northogonal polynomials, namely Jacobi, Gegenbauer, Chebyshev and Legendre\npolynomials. We derive a generalization of the generating function for\nGegenbauer polynomials through extension a two element sequence of generating\nfunctions for Jacobi polynomials. Specializations of generating functions are\naccomplished through the re-expression of Gauss hypergeometric functions in\nterms of less general functions. Definite integrals which correspond to the\npresented orthogonal polynomial series expansions are also given.\n

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